Coding Theory and Algebraic Geometry: Proceedings of the International Workshop held in Luminy, France, June 17–21, 1991

Henning Stichtenoth, Michael A. Tsfasman (auth.), Henning Stichtenoth, Michael A. Tsfasman (eds.)3540556516, 9783540556510, 0387556516

About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting “Algebraic Geometry and Coding Theory” was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.

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Table of contents :
Algebraic geometry and coding theory an introduction….Pages 1-3
Reed-Muller codes associated to projective algebraic varieties….Pages 4-17
Decoding Algebraic-Geometric Codes by solving a key equation….Pages 18-25
On the different of abelian extensions of global fields….Pages 26-32
Goppa codes and Weierstrass gaps….Pages 33-42
On a characterization of some minihypers in PG(t,q) (q=3 or 4) and its applications to error-correcting codes….Pages 43-62
Deligne-Lusztig varieties and group codes….Pages 63-81
Spectra of linear codes and error probability of decoding….Pages 82-98
On the true minimum distance of Hermitian codes….Pages 99-107
Sphere packings centered at S-units of algebraic tori….Pages 108-121
A function field related to the Ree group….Pages 122-131
On the gonality of curves, abundant codes and decoding….Pages 132-144
Curves with many points and multiplication in finite fileds….Pages 145-169
The domain of covering codes….Pages 170-177
Some remarks on the asymptotic number of points….Pages 178-192
On the weights of trace codes….Pages 193-198
Minoration de Certaines Sommes Exponentielles Binaires….Pages 199-209
Linear codes, strata of Grassmannians, and the problems of segre….Pages 210-223